1. DynaMAT Icelandic material Freyja Hreinsdóttir June 14th 2013 http://www.dynamathmat.eu/

2. Icelandic material • Euclidean Eggs • Using sliders to investigate functions, tangents and integrals • Piecewise defined functions • Investigating 2 by 2 matrices – part I • Investigating 2 by 2 matrices– part II

3. Euclidean Eggs • Experiment - have fun • Learn how to use some tools in GeoGebra • Eggs

4. Principle • When is the meeting of the arc smooth? • two_arcs

5. Arcs and circles

6. Arcs and circles

7. Eggs Five-point egg Four-point egg Moss egg Source for Euclidean Eggs: Dixon, R. Mathographics. Basic Blackwell Limited, Oxford, England, 1987

8. Moss egg Moss egg, Variation of a Moss egg

9. Four-point egg

10. Four-point egg

11. GeoGebra files • Four-point egg • Five-point egg • Experiment_circles • Spiral

12. Chapters on linear algebra – Two graphic views Image of the unit square

13. Two graphic views • In GeoGebra 4.0 the option of having two graphic views open at the same time makes it possible to study maps from the plane to plane • Linear maps are particularly easy to study • There are two ways to do this: • defining a 2 x 2 matrix unit_square, determinant • defining the action on one point and using the trace option – this can also be used for nonlinear maps and complex maps

14. Nonlinear map The method above can be used for any transformation, even non-linear ones. Say we want to study the map We define a point E on a line and then the point G = in Graphic view 2. We then put the trace on G and move the point E along the line and watch the image trace out a curve in Graphics 2.

15. Maps from the complex numbers to the complex numbers • We can use a similar method to study maps from C to C, e.g. Image of a line, circle and the boundary of a square